A polariser transmits one orientation; the analyser at angle θ passes I = I₀cos²θ (Malus's law).
Light is a transverse electromagnetic wave whose electric field oscillates perpendicular to its direction of travel. This sandbox sends a wave through a fixed polariser and then a rotatable analyser. Watch the field vector get projected onto each axis and read the transmitted intensity from the live meter.
I = I₀·cos²θ (Malus's law) · E = E₀·cosθ · crossed: θ = 90° → I = 0 · circular: Ex = E₀cos(ωt), Ey = E₀sin(ωt)
Bees and many other insects navigate using the polarisation pattern of the blue sky, an invisible compass that human eyes cannot see — but a rotated polariser reveals it instantly.
Light is a transverse electromagnetic wave: its electric field oscillates perpendicular to the direction of travel. Polarisation describes the orientation of that electric-field oscillation. In linearly polarised light the field stays in one plane; unpolarised light has fields pointing in all transverse directions.
A polariser has a transmission axis and only passes the component of the electric field aligned with that axis. Unpolarised light passing through it emerges linearly polarised along the axis, and its intensity drops to about half.
Malus's law gives the intensity transmitted by a second polariser (the analyser) set at angle θ to the first: I = I₀cos²θ, where I₀ is the intensity after the first polariser. At θ=0 all light passes; at θ=90° none does.
When two polarisers are crossed (θ=90°) the analyser's transmission axis is perpendicular to the incoming polarisation. The projected component is E₀cos90°=0, so cos²90°=0 and no light is transmitted.
The analyser passes only the field component along its axis: E = E₀cosθ. Intensity is proportional to the square of the field amplitude, so I ∝ E² = E₀²cos²θ, giving I = I₀cos²θ.
A quarter-wave plate is a birefringent crystal that retards one polarisation component by a quarter of a wavelength (90° phase). When linearly polarised light enters at 45° to its axes, the two components combine into circular polarisation, where the field vector rotates as the wave travels.
In circularly polarised light the electric-field vector keeps a constant magnitude but rotates uniformly about the propagation direction, tracing a helix. It results from two perpendicular linear components of equal amplitude and a 90° phase difference.
Sunlight scattered by air molecules (Rayleigh scattering) becomes partially polarised, strongest at 90° from the Sun. Polarising sunglasses and a rotated polariser reveal this by darkening parts of the sky.
Light reflected off horizontal surfaces such as water or roads is largely horizontally polarised. Polarised lenses have a vertical transmission axis, so they block this horizontal glare via Malus's law while still passing useful light.
Yes. The light not transmitted is absorbed (or reflected) by the polariser material; it is not destroyed. The cos²θ factor describes only the fraction passed along the transmission axis, and the remaining energy is converted to heat in the polariser.